Question

The angles of a tiangle are $2(x-7)$, $\frac{3}{2}(x-1)$ and $3(x+11)$. Find $x$ and then show that the triangle is isosceles.

• A. $5$
• B. $35$
• C. $15$
• D. $25$

Answer 1

The correct option is D $25$

Given angles of a triangle are

$2(x-7),\frac{3}{2}(x-1),3(x+11)$

Therefore, $2(x-7)+\frac{3}{2}(x-1)+3(x+11)=180$

$\Rightarrow 4x-28+3x-3+6x+66=360$

$\Rightarrow 13x=325$

$\Rightarrow x=25$

Thus, $x$ is $25$.

To prove it as isosceles triangle, two angles must be equal.

Therefore, $2(x-7)=2(25-7)=2\left(18\right)=36$

$\frac{3}{2}(x-1)=\frac{3}{2}(25-1)=36$

and $3(x+11)=3(25+11)=3\left(36\right)=108$

Thus given angles form an isosceles triangle.